$A$ can do $\frac{1}{4}$ of a work in $10$ days. $B$ can do $\frac{1}{3}$ of the work in $20$ days. In how many days can both $A$ and $B$ together do the work?

$A$ does $\frac{4}{5}$ of a work in $20 \, \text{days}$. He then calls in $B$ and they together finish the remaining work in $3 \, \text{days}$. How long would $B$ alone take to do the whole work? (in $\text{days}$)

Machine $P$ can print one lakh books in $8$ hours,machine $Q$ can print the same number of books in $10$ hours,while machine $R$ can print them in $12$ hours. All the machines are started at $9.00$ a.m. while machine $P$ is closed at $11.00$ a.m. and the remaining two machines complete the work. Approximately at what time will the work be finished?

$5$ men or $7$ women can earn $Rs. 5,250$ per day. How much would $7$ men and $13$ women earn per day? (in $Rs.$)

$A$ can do a piece of work in $4\, h$,$B$ and $C$ can do it in $3\, h$,and $A$ and $C$ can do it in $2\, h$. How long will $B$ alone take to do it? (in $h$)

Two men,$A$ and $B$,working together,completed a piece of work. If worked individually,it would have taken them $30$ and $40$ days to complete the work. If they have received a payment of $Rs. 2100$,then $B$'s share is (in $Rs.$)